I'm here to help. Those 3 points all lie on the same line. We know this because if we find the slope between any 2 of those points, it is the same. I'll show you: 
. Now another 2 points: 
. The same holds for the first and third points. So we got that out of the way. Now we will pick any one of those points and use the x and y values and our slope to write an equation of that line and then finally solve for the x and y intercepts. I'm going to use the first point (10, 20): 
. We will simplify to get it into y = mx + b form: 
and 
and finally, 
. The y-intercept exists when x = 0, so when x = 0, y = 36. The x-intercept exists when y = 0, so when y = 0, x = 22.5. In summary, y-intercept: (0, 36). x-intercept: (22.5, 0) and you're all done!
I need help. due in 15
1 answer:
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The time it will take the tank to be empty is;
<em><u>t = 1.26 minutes</u></em>
The image of the initial tank is missing and so i have attached it.
Let's call the area of the hole be A_h
- From conservation of energy, velocity at which water leaves the tank is; v = √2gh
Thus, volumetric rate; = A_h(√2gh)
- If we consider possible friction and contraction, we differentiate to get;
dV/dt = -cA_h(√2gh)
Now, volume of tank is;
V = ¹/₃πr²h
V' = dv/dt = (¹/₃πr²h)dh/dt
Thus; -cA_h(√2gh) = (¹/₃πr²h)dh/dt
- Integrating to get t gives us;
t = (2(√H - √h))/(3c√2g × (r'/r)²)
where;
r' is radius of circular hole = 4 inches = 0.333 ft
h = 0 since the tank has a hole
c = 0.6
g = 32 ft/s²
H = 8 ft
- Since the vertex has an angle of 60°, then a line of symmetry across it divides the angle into two which will be 30° each. We can use trigonometry to find the current radius r.
Thus; r/H = tan 30°
r = 8 tan 30°
r = 4.6188 ft
Thus;
t = (2(√8 - √0))/(3 × 0.6(√2 × 32) × (0.333/4.6188)²)
t = 75.5757 seconds
Converting to minutes gives; t = 1.26 minutes
Read more at; brainly.com/question/24319549
